Braxton was first encountered by the crew of the USS Voyager in 2373 when the Aeon appeared in the Delta Quadrant and attempted to destroy Voyager after Braxton informed CaptainKathryn Janeway and her crew that there was evidence that the Intrepid-class starship was responsible for the Sol system's destruction in the 29th century. Voyager was able to disrupt the Aeon's systems, and was pulled into a temporal rift and crash-landed on Earth in 1967. Braxton was able to escape, but the Aeon fell into the hands of Henry Starling and became irretrievable.

Over the next thirty years, Braxton was forced to live as a tramp and vagrant in 20th centuryLos Angeles, becoming paranoid and aggressive, as he watched Starling use technology from the Aeon to spark a technological revolution and become extremely wealthy in the process. Following Voyager's arrival in 1996, Braxton was able to make contact with Janeway and together they managed to stop Starling in his attempt to take the Aeon to the 29th century, which originally caused the Sol system's destruction.

Voyager's next encounter with Braxton came in late 2375, when the ship was destroyed by a temporal disruptor. Braxton had Seven of Nine transported to the Relativity prior to Voyager's destruction, and enlisted her help in traveling to Voyager at various points in its history to determine who the temporal criminal was who planted the disruptor. It was eventually determined that an older version of Braxton himself was the criminal, having succumbed to temporal psychosis at some point in the future. The original Braxton plus two other versions recovered by the Relativity underwent temporal integration. LieutenantJuel Ducane assured CaptainKathryn Janeway and Seven of Nine that Braxton would stand trial for the crimes that he was going to commit. (VOYepisode: "Relativity")